Numerical Analysis for Critical Structures Protection against Blast Loading Using Metallic Panels

: The need for building protection against blast loads is a crucial issue nowadays due to the escalating threat of terrorist attacks, which a ﬀ ect people’s lives and critical structures. Consequently, design of protective panels to segregate building façades from the e ﬀ ect of a nearby explosion is required. Such design mainly depends on the ability of protective panels to mitigate and di ﬀ ract the blast wave before reaching building façades. Five protective panel models with di ﬀ erent designs, referred to as the Combined Protection System (CPS), are introduced in this paper. The main objective of this research was to achieve a design that could sustain a blast load with minimum plastic deformations. The introduced CPS designs included two steel plates linked by connector plates. The CPS dimensions were 3 m × 3 m × 0.35 m, representing length, width, and height, respectively. After that, the successful panel design was supported by placing these panels onto a masonry wall in di ﬀ erent conﬁgurations. The protective panels were tested against 50 kg of trinitrotoluene (TNT) with a stando ﬀ distance of one meter. The ﬁnal run of the optimum model was carried out using a blast load equivalent to 500 kg of TNT. The air–structure interactions were simulated using ﬁnite element analysis software called “ANSYS AUTODYN”, where the deformation of the panel was the governing parameter to evaluate the behavior of di ﬀ erent designs. The analysis showed minimum deformation of the CPS design with vertical and horizontal connecting plates in a masonry wall distanced at 500 mm from the panel. However, the other designs showed promising results, which could make them suitable for critical structural protection on di ﬀ erent scales.


Introduction
Blast loads have gained attention in recent years due to the large number of deliberate events. Thus, the protection of significant and critical structures, such as governmental buildings and airports, against extreme loads, such as high velocity impacts and explosions, has become a crucial issue. Consequently, the development of new technologies for protecting such structures against blast loads has been of great interest, not only for military applications but also for civilian purposes. The threat from an explosion is defined by the standoff distance and the charge quantity.

Pressures on the Structural Surfaces
The blast load is characterized by the instantaneous release of an enormous amount of energy, and depends on the explosive materials and the basis of their physical state [42]. Explosions are classified as far-range explosions when the offset distance is equal to or greater than 1.2 m/kg 1/3 ; and are classified as near-range explosions when the offset distance is less than 1.2 m/kg 1/3 . Figure 1 represents a typical pressure versus time plot of a blast wave. The blast wave is characterized by a sudden increase in incident pressure to a certain peak value, and the subsequent decay in the atmospheric pressure (positive phase). After that, the incident pressure decays further underneath the ambient atmospheric pressure producing negative phase pressure. The pressure at any instant of time is defined by the modified Friedlander's equation, as presented in Equation (1) where, P(t) is the incident overpressure at any time instant; P 0 is the ambient pressure; P so + and P so − are the peak positive incident overpressure and the peak negative incident under-pressure, respectively; t pos and t neg are the positive and the negative phase durations for the incident blast wave, respectively; t a is the arrival time; and θ is the decay parameter of the wave. Friedlander equation can be used for the positive phase (t 1 ≤ t ≤ t 2 ). The peak side-on overpressure is presented in Equation (2) [43] where K 1 is a constant depending on the quantity of the explosive charge as in [43]. The scaled distance is represented as Z = R/W 1 3 , where the variables R and W refer to the distance from the center of a spherical charge and the charge mass of equivalent TNT, respectively.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 18 any failure. This panel design includes a modified structural design. The modifications include reinforcement techniques using shear connectors and horizontal and vertical walls.

Pressures on the Structural Surfaces
The blast load is characterized by the instantaneous release of an enormous amount of energy, and depends on the explosive materials and the basis of their physical state [42]. Explosions are classified as far-range explosions when the offset distance is equal to or greater than 1.2 m/kg 1/3 ; and are classified as near-range explosions when the offset distance is less than 1.2 m/kg 1/3 . Figure 1 represents a typical pressure versus time plot of a blast wave. The blast wave is characterized by a sudden increase in incident pressure to a certain peak value, and the subsequent decay in the atmospheric pressure (positive phase). After that, the incident pressure decays further underneath the ambient atmospheric pressure producing negative phase pressure. The pressure at any instant of time is defined by the modified Friedlander's equation, as presented in Equation (1) (1) where, P (t) is the incident overpressure at any time instant; P0 is the ambient pressure; Pso + and Pso − are the peak positive incident overpressure and the peak negative incident under-pressure, respectively; tpos and tneg are the positive and the negative phase durations for the incident blast wave, respectively; ta is the arrival time; and θ is the decay parameter of the wave. Friedlander equation can be used for the positive phase t t t . The peak side-on overpressure is presented in Equation where K1 is a constant depending on the quantity of the explosive charge as in [43]. The scaled distance is represented as , where the variables R and W refer to the distance from the center of a spherical charge and the charge mass of equivalent TNT, respectively.

Mathematical Model and Model Hypothesis
Protective panel models consist of two steel plates joined with connectors. The models introduced in this paper are called the Combined Protection System (CPS), which is an extension of a previous model for a protective panel investigated in [44]. The panel design used in this study consisted of two steel plates, each 20 mm in thickness with a steel yield stress of 4.0 × 10 5 kPa. The

Mathematical Model and Model Hypothesis
Protective panel models consist of two steel plates joined with connectors. The models introduced in this paper are called the Combined Protection System (CPS), which is an extension of a previous model for a protective panel investigated in [44]. The panel design used in this study consisted of two steel plates, each 20 mm in thickness with a steel yield stress of 4.0 × 10 5 kPa. The panel dimensions were 3 m tall, 3 m wide, and 350 mm thick. Moreover, the panel was supported at the bottom due to the limitations of deformation in the middle; hence, the bottom fixed support helped in reducing the deformation in the middle of the panel. The parameters were adopted from [44]. Furthermore, the effective charge weight was 50 kg of TNT. The standoff distance between the explosive charge and panels was set to 1 m. The ANSYS AUTODYN finite element analysis package was deployed to simulate the blast wave propagation, due to its ability to study air-structure interactions. The material Appl. Sci. 2020, 10, 2121 4 of 18 properties for the TNT and air were retrieved from the standard AUTODYN library. The modeling of the air was carried out using 3D Euler equations, while the explosive charge was typically modeled using the Jones Wilkens Lee (JWL) equation of state, which can be written as Equation (3) [28,45,46] where P denotes the hydrostatic pressure, v denotes the specific volume, and e denotes the specific internal energy. C 1 , r 1 , C 2 , r 2, and w are the material constants. The values of constants C 1 , r 1 , C 2 , r 2, and w for many common explosives have been previously determined from dynamic experiments. The values of the constants for TNT explosives are available in AUTODYN as shown in Table 1 [28,46,47].
In addition, the air is modeled by an ideal gas equation of state, which can be expressed as in Equation (4) where, γ denotes the heat specific ratio and ρ denotes the density. The standard constants of air were taken from AUTODYN material library, that is, air density, where ρ = 1.225 kg/m 3 and γ = 1.4. The air initial internal energy was assumed to be 2.068 × 10 5 kJ/kg [46]. The material of the steel panel was selected from the ANSYS library. Additionally, the linear equation of state and strength model was applied. The yield stress of the steel panel was assumed to be 4 × 10 8 (Pa). The solver used for steel plates was the shell element. The air element was modeled with dimensions of 4 m, 3 m, and 3 m, representing length, width, and height, respectively. Moreover, movable gauges to measure deformation were added, where the critical gauge position was placed at the mid-point of the panel. During the analysis there was a raised governing variable paradox either pressure or deformation to be considered as governing variable as clarified in Fekry, M. et al. [44]. Furthermore, deformation was selected to be the governing value. Eventually, the boundary condition was set as fixed free from the lower cross-section of the panel. Figure 2 illustrates the model setup.
For accuracy, the model validation was based on the previous work of the authors of [44]. By comparing the results of the verification model and the reference model it was found that the correlation of the results was very strong. The displacement peak value in the reference model was 82 mm and was 79 mm in the verification model [44].

CPS 3
Horizontal and vertical plates were used in a joining method, where the vertical position distance was 750 mm from the edge and the horizontal distance was 500 mm equally spaced. The horizontal and vertical plates had a thickness of 12 mm. Figure 3 represents the orientation of

CPS 3
Horizontal and vertical plates were used in a joining method, where the vertical position distance was 750 mm from the edge and the horizontal distance was 500 mm equally spaced. The horizontal and vertical plates had a thickness of 12 mm. Figure 3 represents the orientation of horizontal and vertical plates inside the panel. The mixed orientation of the joining plates improved the distribution of the load on the front and rear plates; thus, deformation was distributed along the plates. Consequently, the maximum deformation was reduced to 20 mm and occurred at 13 milliseconds. The graph of deformation versus time showed a significant reduction in deformation and achieved promising results, as shown in Figure 4. Figure 5 shows the location of the maximum deformation located in the middle of panel. The vertical plates increased the stiffness in the direction of loading due to the increase in inertia of the panel. Finally, the mixed oriented connectors improved the stiffness of the structure in main stress directions. Plastic deformation in this model varied in distribution between the front, rear, and stiffener plates. Deformation in the front plate recorded a wide plastic region. However, plastic deformation in the rear plate was included in small regions. Furthermore, the deformation in vertical connecting plates was plastic deformation with small elastic regions. The lower horizontal connecting plates achieved a larger plastic deformation region compared to the upper plates. This is because of the proximity of lower plate to the explosive charge. In conclusion, the contribution of the vertical plates was significant. Comparison between the deformation plots for the front, rear, and connector plates is shown in Figures 6-8. Where the green color represents an elastic region and the light blue color represents a plastic region.

CPS 3
Horizontal and vertical plates were used in a joining method, where the vertical position distance was 750 mm from the edge and the horizontal distance was 500 mm equally spaced. The horizontal and vertical plates had a thickness of 12 mm. Figure 3 represents the orientation of horizontal and vertical plates inside the panel. The mixed orientation of the joining plates improved the distribution of the load on the front and rear plates; thus, deformation was distributed along the plates. Consequently, the maximum deformation was reduced to 20 mm and occurred at 13 milliseconds. The graph of deformation versus time showed a significant reduction in deformation and achieved promising results, as shown in Figure 4. Figure 5 shows the location of the maximum deformation located in the middle of panel. The vertical plates increased the stiffness in the direction of loading due to the increase in inertia of the panel. Finally, the mixed oriented connectors improved the stiffness of the structure in main stress directions. Plastic deformation in this model varied in distribution between the front, rear, and stiffener plates. Deformation in the front plate recorded a wide plastic region. However, plastic deformation in the rear plate was included in small regions. Furthermore, the deformation in vertical connecting plates was plastic deformation with small elastic regions. The lower horizontal connecting plates achieved a larger plastic deformation region compared to the upper plates. This is because of the proximity of lower plate to the explosive charge.
In conclusion, the contribution of the vertical plates was significant. Comparison between the deformation plots for the front, rear, and connector plates is shown in Figure 6, Figure 7and

CPS 4
The number of vertical plates was increased to four, equally spaced at 1000 mm, while the number of horizontal plates was kept the same as in the previous model. Figure 9 represents the orientation of horizontal and vertical plates inside the panel. The new panel design improved the deformation distribution, while reducing the regions of plastic deformation in all plates. In addition, the maximum deformation was reduced significantly to 16 mm, occurring 9 milliseconds before the panel started relieving the load. The vertical plates achieved a smaller plastic region compared to the previous model. The design cost of this model would be higher than the previous model, but it withstood the blast load with less damage and without failure. Furthermore, such panels would be able to sustain sequential blast waves, in case of several attacks occurring concurrently. Finally, the CPS results achieved the main goal, which was clearly observed in the deformation graph shown in Figure 10. Figure 11 shows the location of the maximum deformation at the middle of the panel. Moreover, the plastic deformation regions of the rear, front, vertical, and horizontal plates showed promising results matching the aims of the researcher, as shown in Figure 12, Figure 13 and Figure  14.

CPS 4
The number of vertical plates was increased to four, equally spaced at 1000 mm, while the number of horizontal plates was kept the same as in the previous model. Figure 9 represents the orientation of horizontal and vertical plates inside the panel. The new panel design improved the deformation distribution, while reducing the regions of plastic deformation in all plates. In addition, the maximum deformation was reduced significantly to 16 mm, occurring 9 milliseconds before the panel started relieving the load. The vertical plates achieved a smaller plastic region compared to the previous model. The design cost of this model would be higher than the previous model, but it withstood the blast load with less damage and without failure. Furthermore, such panels would be able to sustain sequential blast waves, in case of several attacks occurring concurrently. Finally, the CPS results achieved the main goal, which was clearly observed in the deformation graph shown in Figure 10. Figure 11 shows the location of the maximum deformation at the middle of the panel. Moreover, the plastic deformation regions of the rear, front, vertical, and horizontal plates showed promising results matching the aims of the researcher, as shown in Figures 12-14.

CPS 4 and Masonry Wall with No Distance between Them
The masonry wall used in the model consisted of standard small bricks placed in the wide direction. Cement mortar joined the brick with each other. The wall dimensions were concurrent with the panel dimensions. The panel was separated from the wall by zero distance; it was totally in contact with the front plate. Boundary condition selected for the wall represented a hinged wall, as

CPS 4 and Masonry Wall with No Distance between Them
The masonry wall used in the model consisted of standard small bricks placed in the wide direction. Cement mortar joined the brick with each other. The wall dimensions were concurrent with the panel dimensions. The panel was separated from the wall by zero distance; it was totally in contact with the front plate. Boundary condition selected for the wall represented a hinged wall, as

CPS 4 and Masonry Wall with No Distance between Them
The masonry wall used in the model consisted of standard small bricks placed in the wide direction. Cement mortar joined the brick with each other. The wall dimensions were concurrent with the panel dimensions. The panel was separated from the wall by zero distance; it was totally in contact with the front plate. Boundary condition selected for the wall represented a hinged wall, as shown in Figure 15. Reasons behind the use of a masonry wall include two main points. Firstly for security reasons; in most cases, the panel would be placed on the inner side of the premises' fence wall to work as the main protective component without being visible from the outside. Secondly, a masonry wall would fail once the charge was detonated, which would reduce the intensity of the blast wave before hitting the front panel plates. Consequently, the deformation after adding the masonry wall was reduced significantly, recording a maximum deformation of 13 mm. Figure 16 shows the maximum deformation, which occurred at 11 milliseconds. Furthermore, the deformation first occurred in the mortar of the wall; after that, bricks start failing. Figure 17 shows that the maximum deformation occurred in CPS4 at the end of analysis and failure of the masonry wall. Moreover, the plastic deformation regions of the rear, front, vertical, and horizontal plates were lower than CPS4 because the masonry wall consumed part of blast wave, as shown in  shows the maximum deformation, which occurred at 11 milliseconds. Furthermore, the deformation first occurred in the mortar of the wall; after that, bricks start failing. Figure 17 shows that the maximum deformation occurred in CPS4 at the end of analysis and failure of the masonry wall. Moreover, the plastic deformation regions of the rear, front, vertical, and horizontal plates were lower than CPS4 because the masonry wall consumed part of blast wave, as shown in Figure 18      shows the maximum deformation, which occurred at 11 milliseconds. Furthermore, the deformation first occurred in the mortar of the wall; after that, bricks start failing. Figure 17 shows that the maximum deformation occurred in CPS4 at the end of analysis and failure of the masonry wall. Moreover, the plastic deformation regions of the rear, front, vertical, and horizontal plates were lower than CPS4 because the masonry wall consumed part of blast wave, as shown in Figure 18

CPS 4 and Masonry Wall with 500 mm Distance between Them
CPS 4 presumes that the panel will be installed behind a masonry wall with a distance between them equal to 500 mm. Hence, the previous model was repeated with the same conditions but with a 500 mm distance between panel and masonry wall. This distance allowed the masonry wall to absorb more energy while failing. Figure 21 shows the model setup. The blast swept the wall until hitting the panel as shown in Figure 22. This reduced the blast load effect by a significant value. Consequently, the deformation in the panel achieved near zero deformation. Deformation recorded a maximum value of 2 mm at 5 milliseconds, as shown in Figure 23. Furthermore, the plastic deformation region was obvious where the masonry wall hit the panel at the front plate. Nevertheless, the rear plate showed zero plastic region, which means that the rear plate was functioning after the blast, with no damage. So, the panel could be reversed and not changed until the second incident might happen. This would lead to cost reduction and would double the panel life

CPS 4 and Masonry Wall with 500 mm Distance between Them
CPS 4 presumes that the panel will be installed behind a masonry wall with a distance between them equal to 500 mm. Hence, the previous model was repeated with the same conditions but with a 500 mm distance between panel and masonry wall. This distance allowed the masonry wall to absorb more energy while failing. Figure 21 shows the model setup. The blast swept the wall until hitting the panel as shown in Figure 22. This reduced the blast load effect by a significant value. Consequently, the deformation in the panel achieved near zero deformation. Deformation recorded a maximum value of 2 mm at 5 milliseconds, as shown in Figure 23. Furthermore, the plastic deformation region was obvious where the masonry wall hit the panel at the front plate. Nevertheless, the rear plate showed zero plastic region, which means that the rear plate was functioning after the blast, with no damage. So, the panel could be reversed and not changed until the second incident might happen. This would lead to cost reduction and would double the panel life cycle. However, if the explosive charge weight were doubled, the panel would have extra protection with the same setup at the time of the attack. Figures 24 and 25 show the impact of the blast load on the front and the rear plates. them equal to 500 mm. Hence, the previous model was repeated with the same conditions but with a 500 mm distance between panel and masonry wall. This distance allowed the masonry wall to absorb more energy while failing. Figure 21 shows the model setup. The blast swept the wall until hitting the panel as shown in Figure 22. This reduced the blast load effect by a significant value. Consequently, the deformation in the panel achieved near zero deformation. Deformation recorded a maximum value of 2 mm at 5 milliseconds, as shown in Figure 23. Furthermore, the plastic deformation region was obvious where the masonry wall hit the panel at the front plate. Nevertheless, the rear plate showed zero plastic region, which means that the rear plate was functioning after the blast, with no damage. So, the panel could be reversed and not changed until the second incident might happen. This would lead to cost reduction and would double the panel life cycle. However, if the explosive charge weight were doubled, the panel would have extra protection with the same setup at the time of the attack. Figure 24 and Figure 25 show the impact of the blast load on the front and the rear plates.      The great performance of CPS4 against the 50 kg of TNT allowed the authors to take the model to next level. The model was repeated and examined against a charge weight of 500 kg of TNT. This run helped to study the maximum bearable blast load of the panel. Astonishing results were observed, proving that the panel could protect critical buildings from a charge of up to 500 kg of TNT. Such an explosive charge would emulate a large-scale terrorist attack. Figure 26 shows the deformation versus time of the panel against 500 kg of TNT. The maximum deformation value was 160 mm, occurring at 20 ms. The plastic deformation region of the rear plate is shown in Figure 27. The failure in the masonry wall, the front plate, and the connecting plates are shown in Figure 28, Figure 29 and Figure 30, respectively.
Following the blast wave, the masonry wall was swept until smashing the front plate; the masonry wall was totally destroyed and tore the plate at a lower section. Moreover, the horizontal plate was disintegrated from the middle at the vertical plates. Furthermore, the fragments of all the failed parts crumbled onto the rear plate, causing high plastic deformation. However, the plastic region was very large with no obvious failure occurring in the rear plate. This means that such panels could withstand a charge of up to 500 Kg of TNT. Eventually, this model proved that the CPS4 had a chance to survive a charge that is larger than moderately sized, which is rarely used in suicide attacks.
In conclusion, the research aim has been achieved and validated theoretically. The great performance of CPS4 against the 50 kg of TNT allowed the authors to take the model to next level. The model was repeated and examined against a charge weight of 500 kg of TNT. This run helped to study the maximum bearable blast load of the panel. Astonishing results were observed, proving that the panel could protect critical buildings from a charge of up to 500 kg of TNT. Such an explosive charge would emulate a large-scale terrorist attack. Figure 26 shows the deformation versus time of the panel against 500 kg of TNT. The maximum deformation value was 160 mm, occurring at 20 ms. The plastic deformation region of the rear plate is shown in Figure 27. The failure in the masonry wall, the front plate, and the connecting plates are shown in Figures 28-30, respectively.
Following the blast wave, the masonry wall was swept until smashing the front plate; the masonry wall was totally destroyed and tore the plate at a lower section. Moreover, the horizontal plate was disintegrated from the middle at the vertical plates. Furthermore, the fragments of all the failed parts crumbled onto the rear plate, causing high plastic deformation. However, the plastic region was very large with no obvious failure occurring in the rear plate. This means that such panels could withstand a charge of up to 500 Kg of TNT. Eventually, this model proved that the CPS4 had a chance to survive a charge that is larger than moderately sized, which is rarely used in suicide attacks. In conclusion, the research aim has been achieved and validated theoretically. plate was disintegrated from the middle at the vertical plates. Furthermore, the fragments of all the failed parts crumbled onto the rear plate, causing high plastic deformation. However, the plastic region was very large with no obvious failure occurring in the rear plate. This means that such panels could withstand a charge of up to 500 Kg of TNT. Eventually, this model proved that the CPS4 had a chance to survive a charge that is larger than moderately sized, which is rarely used in suicide attacks. In conclusion, the research aim has been achieved and validated theoretically.

Conclusions
Combined protection systems were investigated against various blast loads in this paper. Panel designs consisted of front and rear steel plates connected with vertical and horizontal stiffeners. Finite element simulation techniques were used to avoid the complexity and expenses of physical tests.
The investigation was simulated using the ANSYS (AUTODYN) finite elements package. The analysis parameters were consistent with the other research parameters, and reflected real cases. The results presented above ensured that all the panels would survive a blast load that would result from 50 kg of TNT without any failure. However, the differences between the various designs were the distribution of plastic deformation region and the maximum deformation values. The concept of placing a solid barrier to decrease the effect of a blast load presented many promising results.
The robust design of the panels showed great performance, not only in resisting a blast wave but also in providing protection from fragments. This will help in improving the safety and security of critical infrastructures without having such protection panels visible. The comparison of various panel designs allowed the authors to select the more robust design and examine it against a higher explosive charge quantity. This resulted in the design withstanding the extreme loading but with total failure of the front plate. With all being said, the presented designs showed outstanding blast wave mitigation capabilities. Moreover, the AUTODYN software showed great ability in studying air-structure interactions with a high-level of accuracy.

Conclusions
Combined protection systems were investigated against various blast loads in this paper. Panel designs consisted of front and rear steel plates connected with vertical and horizontal stiffeners. Finite element simulation techniques were used to avoid the complexity and expenses of physical tests.
The investigation was simulated using the ANSYS (AUTODYN) finite elements package. The analysis parameters were consistent with the other research parameters, and reflected real cases. The results presented above ensured that all the panels would survive a blast load that would result from 50 kg of TNT without any failure. However, the differences between the various designs were the distribution of plastic deformation region and the maximum deformation values. The concept of placing a solid barrier to decrease the effect of a blast load presented many promising results.
The robust design of the panels showed great performance, not only in resisting a blast wave but also in providing protection from fragments. This will help in improving the safety and security of critical infrastructures without having such protection panels visible. The comparison of various panel designs allowed the authors to select the more robust design and examine it against a higher explosive charge quantity. This resulted in the design withstanding the extreme loading but with total failure of the front plate. With all being said, the presented designs showed outstanding blast wave mitigation capabilities. Moreover, the AUTODYN software showed great ability in studying air-structure interactions with a high-level of accuracy.